Ising model with memory: coarsening and persistence properties

TL;DR

This paper investigates how a memory-dependent kinetic Ising model affects coarsening and persistence, revealing that memory introduces energy barriers causing system freezing at zero temperature and an apparent arrest at finite temperatures, yet sharing universality with the standard Ising model.

Contribution

It introduces a memory field into the kinetic Ising model and analyzes its effects on coarsening, persistence, and universality, highlighting local energy barriers and their impact.

Findings

Memory causes energy barriers that freeze the system at zero temperature.

At finite temperature, coarsening is temporarily arrested but eventually proceeds.

The two-point correlation functions are unchanged, indicating same universality class.

Abstract

We consider the coarsening properties of a kinetic Ising model with a memory field. The probability of a spin-flip depends on the persistence time of the spin in a state. The more a spin has been in a given state, the less the spin-flip probability is. We numerically studied the growth and persistence properties of such a system on a two dimensional square lattice. The memory introduces energy barriers which freeze the system at zero temperature. At finite temperature we can observe an apparent arrest of coarsening for low temperature and long memory length. However, since the energy barriers introduced by memory are due to local effects, there exists a timescale on which coarsening takes place as for the Ising model. Moreover the two point correlation functions of the Ising model with and without memory are the same, indicating that they belong to the same universality class.